相关论文: Empirical Bayes Estimation for Lasso-Type Regulari…

Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…

In this paper, we are concerned with regularized regression problems where the prior regularizer is a proper lower semicontinuous and convex function which is also partly smooth relative to a Riemannian submanifold. This encompasses as…

Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…

We investigate how to improve efficiency using regression adjustments with covariates in covariate-adaptive randomizations (CARs) with imperfect subject compliance. Our regression-adjusted estimators, which are based on the doubly robust…

Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…

When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…

We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…

This paper studies the threshold estimation of a TAR model when the underlying threshold parameter is a random variable. It is shown that the Bayesian estimator is consistent and its limit distribution is expressed in terms of a limit…

In the present paper, we derive lower bounds for the risk of the nonparametric empirical Bayes estimators. In order to attain the optimal convergence rate, we propose generalization of the linear empirical Bayes estimation method which…

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating…

After selection with the Group LASSO (or generalized variants such as the overlapping, sparse, or standardized Group LASSO), inference for the selected parameters is unreliable in the absence of adjustments for selection bias. In the…

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…

Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability. We formulate a Distributionally Robust Optimization (DRO) problem which recovers…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…

Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…

Existing Bayesian models, especially nonparametric Bayesian methods, rely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations. While priors can affect posterior distributions through…

In this paper, we introduce a unified framework, inspired by classical regularization theory, for designing and analyzing a broad class of linear regression approaches. Our framework encompasses traditional methods like least squares…

The least-absolute shrinkage and selection operator (LASSO) is a regularization technique for estimating sparse signals of interest emerging in various applications and can be efficiently solved via the alternating direction method of…